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math.NT2021
Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic
Peter Zenz
We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth, compactly supported test functions. The variance is related to an averaged shifted-co…
math.NT2021
Sharp bound for the fourth moment of holomorphic Hecke cusp forms
Peter Zenz
We prove that the fourth moment of holomorphic Hecke cusp forms is bounded provided that the Riemann Hypothesis holds for an appropriate degree 8 L-function. We accomplish this usi…